It is " ... born of water AND of the Spirit". I have always held that verse to mean we accept Christ as our savior and be baptized (Full disclosure: I was a practicing Baptist until about the age of 13)
It is all part of one rebirth. Do you not find it significant that Jesus himself was baptized
You were born of a woman whose water broke.
If you have trusted Jesus Christ as Saviour, You are born of the Spirit.
If you asked Jesus to Save you and got baptized to be Saved, you may or may not be saved. I would have no idea whether you trusted Christ, got Baptized and then someone and then were taught the false doctrine of baptismal regeneration or were trusting baptisn from the beginning.
The first is how I was taught. I trusted Jesus Christ to save me, and then I was taught the (yo yo) work and sinlessness required to go to Heaven.